Mycobacterium tuberculosis, the causative agent of human tuberculosis, is forced into latency by nitric oxide produced by macrophages during infection. In response to nitrosative stress M. tuberculosis has evolved a defense mechanism that relies on the oxygenated form of "truncated hemoglobin" N (trHbN), formally acting as NO-dioxygenase, yielding the harmless nitrate ion. X-ray crystal structures have shown that trHbN hosts a two-branched protein matrix tunnel system, proposed to control diatomic ligand migration to the heme, as the rate-limiting step in NO conversion to nitrate. Extended molecular dynamics simulations (0.1 micros), employed here to characterize the factors controlling diatomic ligand diffusion through the apolar tunnel system, suggest that O2 migration in deoxy-trHbN is restricted to a short branch of the tunnel, and that O2 binding to the heme drives conformational and dynamical fluctuations promoting NO migration through the long tunnel branch. The simulation results suggest that trHbN has evolved a dual-path mechanism for migration of O2 and NO to the heme, to achieve the most efficient NO detoxification.